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First published 2009 Elsevier Limited. All rights reserved.

No part of this publication may be reproduced or transmittedin any form or by any means, electronic or mechanical,including photocopying, recording, or any information storageand retrieval system, without permission in writing from thepublisher. Permissions may be sought directly from ElseviersRights Department: phone: (1) 215 239 3804 (US) or(44) 1865 843830 (UK); fax: (44) 1865 853333; e-mail:[email protected] may also complete your

request online via the Elsevier website at http://www.elsevier.com/permissions.

ISBN 978 0 7020 3032 1

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the BritishLibrary

Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library ofCongress

Notice

Neither the Publisher nor the Editors/Authors assume anyresponsibility for any loss or injury and/or damage to personsor property arising out of or related to any use of the materialcontained in this book. It is the responsibility of the treatingpractitioner, relying on independent expertise and knowledgeof the patient, to determine the best treatment and method ofapplication for the patient.

The Publisher

Printed in China
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It gives me great pleasure to introduce you to Functional Anatomy, the

fi rst book in the Pocket Podiatryseries. The vision of Robert Edwards,

the then Commissioning Editor for Podiatry at Elsevier, the series will see

volumes published over the next 5 years or so. These will build into a

highly informative and clinically-oriented reference library for both under-

and post-graduate podiatrists alike, as well as those from other disci-

plines who are involved in the management of foot, ankle and lower limb

disorders. Other titles in the series include Gait, The Ageing Foot, ThePaediatric Foot, Examination and Diagnosis, Pharmacology, Footwear

and Orthoses, and Podiatric Surgery. It is perhaps indicative of the

progress, and current status, of Podiatry that a series providing such

breadth of information can be presented as refl ecting the true scope of

clinical practice, and as representing vital knowledge for contemporary

clinical practise.

This fi rst volume, concerned with Functional Anatomy, is an entirely

appropriate series opener: podiatrists are only too aware of the impor-tance of the weight bearing function of the foot, and its functional com-

plexity. This volume reviews the nature of the stresses applied to the foot,

their impact on various tissues, how they are managed, and how pathol-

ogy can result from functional impairment. The author, James Watkins, is

Professor of Biomechanics at Swansea University, but has a long history

of involvement with Podiatry through a previous post in Glasgow which

saw him teach the principles of mechanics to undergraduate Podiatrists

for many years. This places him in a unique position to reconcile the sci-

ence of biomechanics with the demands of clinical practice, and the lucid

way in which this is achieved makes this volume an exciting and welcome

addition to the Podiatric literature.

Professor Watkins is one of a team of writers recruited to the project

who rank as some of the brightest talents working within, or with, the

Podiatry profession. Each has substantial experience and a passion for

their subject that is conveyed in their writing, and it is an enviable position

I fi nd myself in, being involved in the development of the manuscripts.

I hope that, as more volumes are published, you judge the series to bethe valuable companion to clinical podiatry it is designed to be and that

your patients benefi t.

Ian Mathieson

Foreword

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Human movement is brought about by the musculoskeletal system

(bones, joints, skeletal muscles) under the control of the nervous sys-

tem. The bones of the skeleton are linked together at joints in a way that

allows them to move relative to each other. The skeletal muscles pull on

the bones in order to control the movements of the joints and, in doing

so, control the movement of the body as a whole. By coordinated activ-

ity of the various muscle groups, forces generated by the muscles are

transmitted by the bones and joints to enable the individual to maintainan upright or partially upright posture, move from one place to another

and manipulate objects.

The open-chain arrangement of the bones of the skeleton maximizes

the range of possible body postures. However, this movement capability

is only possible at the expense of low mechanical advantage of skeletal

muscles, which results in relatively high forces in all components of the

musculoskeletal system in most postures and movements. In response to

the forces exerted on them, the musculoskeletal components experiencestrain (deformation). Under normal circumstances, the musculoskeletal

components adapt their size, shape and structure to readily withstand the

strain of everyday physical activity. This process is referred to as struc-

tural adaptation and is continuous throughout life. In the absence of dis-

ease, structural adaptation tends to maintain normal function. However,

the capacity of the musculoskeletal components, especially bone, to

undergo structural adaptation decreases with age. Consequently, strain

that would normally result in structural adaptation in a young person mayresult in tissue degeneration and dysfunction in an older person.

In weightbearing activities, the function of the musculoskeletal system

is to transmit the weight of the body to the ground by creating ground

reaction forces at the feet to maintain upright posture and move the

body in the intended direction. In walking, and other forms of locomotion

such as running, hopping and jumping, the feet act alternately as shock

absorbers, to cushion the impact of the foot with the ground, and pro-

pulsion mechanisms, to propel the body in the desired direction. These

distinct functions are refl ected in the fl exible arched structure of the foot,

which is indicative of the essence of functional anatomy, i.e. the intimate

relationship between the structure and function of the musculoskeletal

system. Accurate diagnosis and appropriate treatment of disorders of

the musculoskeletal system depends largely on the clinicians knowledge

and understanding of this relationship.

Preface

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The purpose of this book is to develop knowledge and understanding

of functional anatomy with particular reference to the foot. The book is

primarily designed as a course text for undergraduate students of podia-

try, but it also has a great deal to offer the practising podiatrist and other

healthcare professionals, in particular, physiotherapists and occupational

therapists, who deal with the acute and chronic effects of lower limb

musculoskeletal pathology.

The book has seven chapters. Chapter 1 describes the elementary

mechanical concepts and principles that underlie human movement,

which are referred to throughout the book. Chapter 2 describes the

basic structure of the body in relation to tissues, organs and systems.

Chapter 3 describes the bones of the skeleton and, in particular, the fea-tures of the bones associated with force transmission and relative motion

between bones. Chapter 4 describes the structure and functions of the

various connective tissues, with particular reference to structural adapta-

tion in bone. Chapter 5 describes the structure and function of the vari-

ous types of joint. Chapter 6 describes the structure and function of the

neuromuscular system. Chapter 7 describes the structure of the foot

and, in particular, the function of the foot in walking.

No previous knowledge of functional anatomy is assumed. To aidlearning, the book features a content overview at the start of each chap-

ter, key concepts highlighted within the text, extensive use of illustrations,

review questions, references to guide further reading, and an extensive

glossary and index.

James Watkins

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Acknowledgements

Thank you to the series editor Dr Ian Mathieson and all of the staff at

Elsevier who contributed to the commissioning and production of the

book. Thanks also to my academic colleagues and the large number of

students who have helped me, directly and indirectly, over many years,

to develop and organize the content of the book.

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C H A P T E R

Elementarybiomechanics

All movements and changes in movement are

brought about by the action of forces. In humanmovements, we interact with the environment

largely through pulling forces (e.g. opening a

fridge door, closing a car door from the inside),

pushing forces (e.g. closing a fridge door,

climbing a fl ight of stairs), pressing forces (e.g.

ringing a door-bell, pressing a key on a key-

board) or combinations of pressing forces (e.g.

gripping a pen or the handle of a cup). Humanmovement is brought about by the neuromus-

culoskeletal system, i.e. the musculoskeletal

system (bones, joints, skeletal muscles) under

the control of the nervous system. The bones

of the skeleton are linked together in a way

that allows them to move relative to each other.

The skeletal muscles pull on the bones in order

to control the movements of the joints and, in

doing so, control the movement of the body as

a whole. By coordinated activity between the

various muscle groups, forces generated by

the muscles are transmitted by the bones and

joints to enable us to maintain an upright or

partially upright posture (e.g. standing, sitting),

move from one place to another (e.g. crawl-

ing, walking, running, swimming) and manipu-

late objects (e.g. carrying a bag, lifting a box,

pushing a wheelbarrow, driving a car, threading

a needle).

The open-chain arrangement of the bones

of the skeleton maximizes the range of pos-

sible body postures. However, this movement

Chapter contents

1Force 2

Mechanics and

biomechanics 3

Forms of motion 6

Units of measurement 7

Newtons laws of motion 9

Newtons law of

gravitation 12

Centre of gravity 13Stability 14

Load, strain and stress 18

Friction 23

Musculoskeletal system

function 30

Centre of pressure 33

Vector and scalar

quantities 33

Moment of a force 40Achilles tendon force and ankle

joint reaction force in upright

standing 46

Levers 48

Load on the musculoskeletal

system 51

Review questions 52

References 52
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1 ELEMENTARY BIOMECHANICS2

capability is only possible at the expense of low mechanical advantage of

skeletal muscles, which results in relatively high forces in all components

of the musculoskeletal system in most postures and movements. Under

normal circumstances the musculoskeletal components adapt their size,

shape and structure to more readily withstand the time-averaged forces

exerted on them, i.e. there is an intimate relationship between the struc-

ture and function of the musculoskeletal system. To understand this rela-

tionship, it is necessary to understand elementary biomechanics. The

purpose of this chapter is to develop knowledge and understanding of

elementary biomechanical concepts and principles.

Force

All bodies, animate and inanimate, are continuously acted upon by forces.

A force can be defined as that which alters or tends to alter a bodys

state of rest or type of movement. For example, in a stationary sitting

position, body weight exerts a constant downward force acting on the

body is counteracted by upward forces exerted on the body by the seat,

the floor beneath the feet and, perhaps, arm rests supporting the arms. Ina standing position, the body is prevented from collapsing by the forces

in the skeletal muscles that stabilize the joints. In order to start walk-

ing forward from a stationary standing position, it is necessary to push

backwards against the ground; the more forcibly we push backward

against the ground, the faster we move forward. Climbing stairs involves

a succession of downward pushes against the stairs.

The forces that act on a body arise from interaction of the body with

its environment. There are two types of interaction: contact interaction,which produces contact forces, and attraction interaction, which pro-

duces attraction forces (Watkins 2007). Contact interaction refers to

physical contact between the body and its environment, such as the

contact forces between our feet and the floor when standing, walking,

running and jumping. Attraction interaction refers to naturally occurring

forces of attraction between certain bodies that tend to make the bod-

ies move towards each other and to maintain contact with each other

after contact is made. For example, a magnetized piece of iron attracts

other pieces of iron to it by the attraction force of magnetism. The human

body is constantly subjected to a very considerable force of attraction,

i.e. body weight, the force due to the gravitational pull of the earth. It is

body weight that keeps us in contact with the ground and which brings

us back to the ground should we leave it, e.g. following a jump into

the air.
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Mechanics and biomechanics 3

Mechanics and biomechanics

Forces tend to affect bodies in two ways (Watkins 2007):

l They tend to deform bodies, i.e. change the shape of the bodies by

stretching, squashing, bending or twisting. For example, squeezing a

tube of toothpaste changes the shape of the tube.

l They determine the movement of bodies, i.e. the forces acting on a

body determine whether it moves or remains at rest and determine its

speed and direction of movement if it does move.

Mechanics is the study of the forces that act on bodies and the effects

of the forces on the size, shape, structure and movement of the bodies.The actual effect that a force or a combination of forces has on a body,

i.e. the amount of deformation and change of movement that occurs,

depends upon the size of the force in relation to the mass of the body

and the mechanical properties of the body.

The mass of a body is the product of its volume and its density. The

volume of a body is the amount of space that the mass occupies and its

density is the concentration of matter (atoms and molecules) in the mass,

i.e. the amount of mass per unit volume. The greater the concentrationof mass, the larger the density. For example, the density of iron is greater

than that of wood and the density of wood is greater than that of poly-

styrene. Similarly, with regard to the structure of the human body, bone is

more dense than muscle and muscle is more dense than fat.

The mass of a body is a measure of its inertia, i.e. its reluctance to

start moving if it is at rest and its reluctance to change its speed and/or

direction if it is already moving. The larger the mass, the greater the iner-

tia and, consequently, the larger the force that will be needed to move

the mass or change the way it is moving. For example, the inertia of a

stationary football (a small mass) is small in comparison to that of a heavy

barbell (a large mass), i.e. much more force will be required to move the

barbell than to move the ball.

Whereas the effect of a force on the movement of a body is largely

determined by its mass, the amount of deformation that occurs is largely

All bodies, animate and inanimate, are continuously acted upon by

forces which arise from interaction of the body with its environment.

The environment exerts two kinds of forces, contact forces and

attraction forces

KeyConcepts
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determined by its mechanical properties, in particular, its stiffness (the

resistance of the body to deformation) and strength (the amount of force

required to break the body). For a given amount of force, the higher the

stiffness and the greater the strength of a body, the smaller the deform-

ation that will occur.

Biomechanics is the study of the forces that act on and within living

organisms and the effect of the forces on the size, shape, structure and

movement of the organisms (Watkins 2007). In relation to humans, bio-

mechanics is the study of the relationship between the external forces

(due to body weight and physical contact with the environment) and

internal forces (active forces generated by muscles and passive forces

exerted on connective tissues) that act on the body and the effect ofthese forces on the size, shape, structure and movement of the body.

Mechanics is the study of the forces that act on bodies and the

effects of the forces on the size, shape, structure and movement of

the bodies

KeyConcepts

Sub-disciplines of mechanics

The different types and effects of forces are reflected in four overlapping

sub-disciplines of mechanics: mechanics of materials, fluid mechanics,

statics and dynamics. Mechanics of materials is the study of the mechan-

ical properties (strength, stiffness, resilience, toughness) of materials.

Mechanics of materials includes, for example, the study of materials used

to make shoes, materials used to make orthoses to be worn in shoes totreat certain foot disorders, and the effects of ageing on bone, muscle and

connective tissues. Fluid mechanics is the study of: (1) the forces that affect

the movement of liquids and gases, such as the flow of water in a pipe or

blood flow in the cardiovascular system; and (2) the effect of liquids and

gases on the movement of solids, such as the movement of the human

body through water and air. Statics is the study of bodies under the action

of balanced forces, i.e. study of the forces acting on bodies that are at rest

or moving with constant speed in a particular direction. In these situations,

the resultant force (the net effect of all the forces) acting on the body is zero.

Figure 1.1Ashows a man standing upright. Since the man is at rest, there are

only two forces acting on him, the weight of his body Wacting downward

and the upward reaction force R1exerted by the ground. The magnitude of

Wand R1 is the same, but they act in opposite directions and, therefore,

cancel out, such that the resultant force acting on the man is zero.
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Mechanics and biomechanics 5

Dynamics is the study of bodies under the action of unbalanced forces,

i.e. bodies moving with non-constant speed. In this situation, the result-

ant force acting on the body will be greater than zero, i.e. the body will

be accelerating (speed increasing) or decelerating (speed decreasing) in

the direction of the resultant force. For example, as the man in Figure 1.1A

is at rest, the resultant force acting on him will be zero. As he starts to

walk (Figure 1.1B), he will be accelerated forward under the action of theresultant force acting on his body, i.e. the resultant of his body weight W

and the force acting on his right foot R2.

Kinematics is the branch of dynamics that describes the movement

of bodies in relation to space and time (Gk. kinema, movement). A kin-

ematic analysis describes the movement of a body in terms of distance

(change in position), speed (rate of change of position) and acceler-

ation (rate of change of speed). Kinetics is the branch of dynamics that

describes the forces acting on bodies, i.e. the cause of the observedkinematics (Gk.kinein, to move).

R1 R2

W W

A B

Figure 1.1 (A) The forces acting on a man standing upright and (B) just after starting to walk.Wbody weight, R1and R2ground reaction forces.

There are four overlapping sub-disciplines of mechanics: mechanics

of materials, fluid mechanics, statics and dynamics

KeyConcepts
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Forms of motion

There are two fundamental forms of motion, linear motion and angular

motion. Linear motion, also referred to as translation, occurs when all

parts of a body move the same distance in the same direction in the same

time (Watkins 2007). In all types of self-propelled human movement, such

as walking, running and swimming, the orientation of the body segments

to each other continually changes and, therefore, pure linear motion sel-

dom occurs in human movement. The human body may experience pure

linear motion for brief periods in activities such as ski-jumping (Figure 1.2).

When the linear movement is in a straight line, the motion is called rectilin-

ear motion (Figure 1.2A). When the linear movement follows a curved path,the motion is referred to as curvilinear motion (Figure 1.2B).

Angular motion, also referred to as rotation, occurs when a body or

part of a body, such as an arm or a leg, moves in a circle or part of

A

B

Figure 1.2 Linear motion: a ski jumper is likely to experience rectilinear motion on therunway (A) and curvilinear motion during flight (B).
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Units of measurement 7

a circle about a particular line in space, referred to as the axis of rota-

tion, such that all parts of the body move through the same angle in the

same direction in the same time. The axis of rotation may be stationary

or it may experience linear motion (Figure 1.3). Most whole body human

movements are combinations of linear and angular motion. For example,

in walking, the movement of the head and trunk is fairly linear, but the

movements of the arms and legs involve simultaneous linear and angular

motion as the body as a whole moves forward (Figure 1.4). The movement

of a multi-segmented body, like the human body, which involves simulta-

neous linear and angular motion of the segments, is usually referred to

as general motion.

There are two fundamental forms of motion, linear motion and angu-

lar motion. Most whole body human movements are combinations of

linear and angular motion

KeyConcepts

Units of measurement

Commerce and scientific communication are dependent on the correct

use and interpretation of units of measurement. With the advent of the

industrial revolution in the 18th century and the progressive increase in

international trade that resulted from it, the need for uniformity in meas-

urement became increasingly evident. At that time, one of the most

widely used systems of units was the British imperial system, but lack of

clarity and consistency with regard to definitions and symbols for manyvariables resulted in resistance to the use of this system internationally

(Rowlett 2004). The metric system of measurements originated in France

around 1790. The name of the system is derived from the base unit for

length, i.e. the metre, which was defined as one ten-millionth of the dis-

tance from the equator to the North Pole. In contrast to the British imper-

ial system, each unit in the metric system has a unique definition and a

unique symbol. Largely for this reason, the metric system progressively

gained ground internationally. The metric system was officially adopted in

the Netherlands and Luxembourg in 1820 and in France in 1837. In 1875,

many of the industrialized countries signed the Treaty of the Metre, which

established the International Bureau of Weights and Measures (BIPM

for Bureau International des Poids et Mesures) and a single system of

units, the International System of Units, to include all physical and chem-

ical, metric and non-metric units. The system is usually referred to as the
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S

E

B

A

E

Figure 1.3 Angular motion: as the arm swings from position A to position B the upper armrotates through an angle qabout the transverse (side-to-side) axis S through the shoulderjoint and the lower arm and hand rotate through an angle about the transverse axis Ethrough the elbow joint.

A B C

Figure 1.4 General motion: in walking, the movement of the head and trunk is fairly linear,but the movements of the arms and legs involve simultaneous linear and angular motion.

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SI system after its French language name Systeme International dUnites.

The SI system is now the most widely used system of units, especially

in science and international commerce. The system is maintained and

updated by the BIPM as new units are proposed and accepted. The

system now consists of a large number of units, but all of the units are

derived from a set of base units. The base units for mechanical varia-

bles in the SI system are the metre (length), the kilogram (mass) and the

second (time). These three units give rise to a sub-section of the SI sys-

tem called the metre-kilogram-second (m-kg-s) system. The correspond-

ing sub-section of the British imperial system is the foot-pound-second

(ft-lb-s) system. These two sub-systems are shown in Table 1.1. Apart

from in a few examples, the m-kg-s system is used in this book. In equa-tions, a decimal point is used to indicate multiplication of one SI unit by

another, e.g. N.m for newton metre.

The International System of Units (SI system) includes all physical

and chemical, metric and non-metric units. It is the most widely used

system of units, especially in science and international commerce

KeyConcepts

Newtons laws of motion

Irrespective of the number of forces acting on a body, the resultant

force acting on a body at rest is zero. A body at rest will only begin to

move when the resultant force acting on it becomes greater than zero.

Similarly, the resultant force acting on a body that is moving with uni-form linear velocity, i.e. in a straight line with constant speed, is also zero.

It will only change direction, accelerate or decelerate when the resultant

force acting on it becomes greater than zero. Furthermore, the amount of

change in speed and/or direction that occurs will depend upon the mag-

nitude and direction of the resultant force, i.e. there is a direct relation-

ship between change of resultant force and change in movement. Isaac

Newton (16421725) described this relationship in what has come to be

known as Newtons laws of motion.

Newtons first law of motion

To move an object from rest or to change the way it is moving, it is

necessary to change the pattern of forces acting on the object. This is

the basis of Newtons first law of motion.
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Table 1.1 Mechanical units and (symbols) of measurement

Quantity British imperial system SI system

Distance foot (ft) metre (m)

Time second (s) second (s)

Speed feet per second (ft/s) metres per second (m/s)

Acceleration feet per second per second

(ft/s2)

metres per second per

second (m/s2)

Mass pound (lb) kilogram (kg)

Linear momentum pounds feet per second (lb.ft/s) kilogram metres per second

(kg.m/s)

Force poundal (pdl) newton (N)

1 pdl 1 lb 1 ft/s2 1 N 1 kg 1 m/s2

Weight* pound force (lbf) kilogram force (kgf)

1 lbf 1 lb 32.2 ft/s2

32.2 pdl

1 kgf 1 kg 9.81 m/s2

9.81 N

Pressure pounds force per square inch

(lbf/in2)

pascal (Pa) (Pa N/m2)

Angular distance radian (rad) radian (rad)

Angular speed radians per second (rad/s) radians per second (rad/s)

Angular acceleration radians per second per second

(rad/s2)

radians per second per

second (rad/s2)

Moment of inertia pound foot squared (lb.ft2) kilogram metres squared

(kg.m2)

Angular momentum pound foot squared per second

(lb.ft2/s)

kilogram metres squared per

second (kg.m2/s)

Turning moment poundal foot (pdl.ft) newton metre (N.m)

Energy and work foot poundal (ft.pdl) joule (J) (J N.m)

Power horsepower (hp)

1 hp 550 ft lb/swatt (W) (W J/s)

*Pound force (lbf) and pound weight (lbwt) are different names for the same unit, i.e. the weight of a

mass of 1 lb. Kilogram force (kgf), kilopond (kp) and kilogram weight (kgwt) are different names for thesame unit, i.e. the weight of a mass of 1 kg.The horsepower symbol is usually written as ft lb/s, but the lb is actually lbf (pound force).

Consequently, the correct symbol for horsepower is ft lbf/s (foot pounds force per second). Fortunately,the horsepower is rarely used in biomechanics.

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An object remains at rest or continues to move with constant velocity(constant speed in a straight line) unless compelled to move or changethe way it is moving by a change in the pattern of forces acting upon it.

For example, a book resting on a table will remain at rest until someone

moves it. A passenger travelling in a bus moves at the same velocity as

the bus. If the bus suddenly brakes the passenger will be thrown for-

ward, especially a standing passenger, since he will tend to move for-

ward with the velocity that the bus had immediately before braking.

Newtons second law of motion

The product of an objects mass m and linear velocity v is referred to

as the linear momentum m.v of the object. Any change in the velocity

of an object results in a change in the linear momentum of the object.

Newtons second law of motion describes the relationship between the

change in linear momentum experienced by an object and the force

responsible for the change.

When a force acts on an object the change in linear momentumexperienced by the object takes place in the direction of the forceand is proportional to the magnitude and duration of the force.

This statement can be expressed algebraically as F.t m.v2 m.v1,

where Fmagnitude of the force, tduration of the force, mmass

of object, v1velocity of object immediately prior to application of the

force, and v2velocity of object immediately after removal of the force.

The product of force and time, F.t, is referred to as the impulse of the

force. As a(v2 v1)/t, where athe average acceleration (rate ofchange of velocity) of the object during the impulse F.t, then Newtons

second law of motion can also be expressed algebraically as F m.a. If

v2was greater than v1, i.e. the velocity of the object increased as a result

of the impulse, then a is positive. If v2was less than v1, i.e. the velocity

of the object decreased as a result of the impulse, then a is negative.

Negative acceleration is usually referred to as deceleration.

Newtons third law of motionObjects in contact exert equal and opposite forces on each other. This is

Newtons third law of motion.

When one object exerts a force on another there is an equal andopposite force exerted by the second object on the first.

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Newtons law of gravitation

In addition to the three laws of motion, Newtons law of gravitation

describes the naturally occurring force of attraction that is always present

between any two bodies.

Every body attracts every other body with a force which varies directlywith the product of the masses of the two bodies and inversely with the

square of the distance between them.

Thus, the force of attraction Fbetween two objects of massesm1andm2

at a distance dapart is given by F(G.m1.m2)/d2where G is a constantreferred to as the Gravitational Constant and dis the distance between the

centres of mass of the two bodies. In very simple terms, the law of gravi-

tation means that the force of attraction between any two bodies will be

greater the larger the masses of the bodies and the closer they are together.

It is, perhaps, hard to appreciate that a force of attraction exists between

any two bodies. However, the force of attraction between bodies is nor-

mally minute and has no effect on the movement of the bodies. There is,

however, one body that results in a significant force of attraction betweenitself and other bodies, i.e. the earth. In relation to the law of gravitation, the

earth is simply a massive body (radius 6.37 103km; Elert 2000) with a

huge mass (5.98 1024kg; Elert 2000). Even though the distance between

the centre of the earth (assumed to be the centre of mass of the earth) and

any body on the surface of the earth (or in space close to the surface of the

earth) is extremely large, the force of attraction between the earth and any

other body is much larger than that which exists between any two bodies

on or close to the earths surface. This is due to the huge mass of the earth.

The force of attraction between the earth and any other body is not large

enough to have any effect on the movement of the earth, but it is certainly

large enough to pull any body towards the earth. The force of attraction

between the earth and any body is referred to as the weight of the body.

This is the force of attraction that keeps us in contact with the earth or

brings us back to the surface of the earth very quickly should we momen-

tarily leave it as, for example, when jumping off the ground. By the law of

gravitation, the weight W of an object of mass m may be expressed as

W m(G.M/d2) where Mmass of the earth and ddistance betweenthe centre of the earth and the object on its surface. The term G.M/d2

is usually referred to as gravity, g(not to be confused with G) which is the

acceleration due to the earths gravitational field, i.e. when an object is

held above the ground and then released, it will accelerate downward at

9.81 m/s2. The weight Wof a massmis usually expressed as W m.g.

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Centre of gravity 13

Units of force

In the metric system, the unit of force is the newton (N). A newton is

defined as the force acting on a mass of 1 kg that accelerates it at 1 m/s2,

i.e. 1 N 1 kg 1 m/s2. Since the acceleration due to gravity is 9.81 m/s2

it follows that the weight of a mass of 1 kg, referred to as 1 kgf (kilogram

force: see Table 1.1), is given by

1 1 9 81 9 812kgf kg m/s N . .

A mass of 1 kg is equal to 2.2046 lb, i.e. 1 kgf 2.2046 lbf (pound force).The kgf and lbf are referred to as gravitational units of force. Body weight

is often recorded in kg or lb, which are units of mass. While this makes

no practical difference, the correct units for weight are kgf or lbf (Watkins

2007).

Centre of gravity

The human body consists of a number of segments linked by joints. Each

segment contributes to the bodys total weight (Figure 1.5A). Movement of

the body segments relative to each other alters the weight distribution of

the body. However, in any particular body posture the body behaves (in

terms of the effect of body weight on the movement of the body) as if the

total weight of the body is concentrated at a single point called the cen-

tre of gravity (also referred to as centre of mass) (Figure 1.5B). Body weight

acts vertically downward from the centre of gravity along a line called the

line of action of body weight. The concept of centre of gravity applies to

all bodies, animate and inanimate.

The centre of gravity of an object is the point at which the whole

weight of the object can be considered to act

KeyConcepts

The position of an objects centre of gravity depends on the distribution

of the weight of the object. For a regular-shaped object with uniform

density such as a cube, oblong or sphere, the centre of gravity is located

at the objects geometric centre. However, if the object has an irregular

shape or non-uniform density, like the human body, the position of the

centre of gravity will reflect the mass distribution and it may be inside or
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Stability 15

respect to the base of support ABCD in the positions shown in Figure

1.7B and C, and unstable with respect to the base of support ABCD in theposition shown in Figure 1.7D.

A B

Figure 1.6 Position of the whole body centre of gravity when standing upright (A) and bend-ing forward (B).

With respect to a particular base of support, an object is stable when

the line of action of its weight intersects the plane of the base of sup-

port and unstable when it does not

KeyConcepts

With regard to human movement, the terms stability and balance are often

used synonymously. Maintaining stability of the human body is a fairly

complex, albeit largely unconscious, process (Roberts 1995). When stand-

ing upright the line of action of body weight intersects the base of sup-

port formed by the area beneath and between the feet (Figure 1.8A and B).

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The size of the base of support can be increased by moving the feet fur-

ther apart. For example, moving one foot to the side increases side-to-side

stability (Figure 1.8C) and moving one foot in front of the other increases

anteroposterior stability (Figure 1.8D).In general, the lower the centre of gravity and the larger the area of the

base of support, the greater the stability. The recumbent position is the

most stable position of the human body since it is the position in which

the area of the base of support is greatest and the height of the cen-

tre of gravity lowest. The degree of muscular effort needed to maintain

stability tends to decrease as the area of the base of support increases.

For example, it is usually easier, in terms of muscular effort, to maintain

stability when standing on both feet than when standing on one foot.

Similarly, it is usually less tiring to sit than to stand, and less tiring to lie

down than to sit. A person recovering from a leg injury may use crutches

or a walking stick in order to relieve the load on the injured limb. The use

of crutches or a walking stick also increases the area of the base of sup-

port and makes it easier for the user to maintain stability (Figure 1.8E and F).

Movement of the body from one base of support to another, such

as in moving from standing to sitting, illustrates the unconscious way

in which the balance systems of the body automatically redistribute

body weight to maintain stability. Figure 1.9shows a person moving froma standing position to sitting on a chair. The person moves his feet close

to the front of the chair and then lowers his body by flexing his knees

and bending his trunk forward while maintaining the same base of sup-

port, i.e. the area beneath and between his feet (Figure 1.9A and B). He

may or may not take hold of the sides of the chair as his thighs approach

the seat of the chair. If he does take hold of the chair, his base of support

A B

D E

C

A

D

B

C

AW

B

A

A

B

A

B B

Figure 1.7 The line of action of the weight of a cube in relation to its base of support.

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Stability 17

A

B C D

E F

Figure 1.8 The line of action of body weight in relation to the base of support. (A, B) Standingupright. (C) Standing upright with feet apart, side-by-side. (D) Standing upright with the leftfoot in front of the right foot. (E) Standing with the aid of a walking stick in the right hand.(F) Standing with the aid of crutches or two walking sticks. The symboldenotes the point ofintersection of the line of action of body weight with the base of support.

A B C D

Figure 1.9 The line of action of body weight in relation to the base of support when movingfrom standing to sitting.

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immediately increases to include the area bounded by the legs of the

chair as well as that beneath and between his feet, but the line of action

of his body weight will still be over the area between his feet (Figure 1.9C).

When his thighs come close to the seat of the chair he begins to transfer

his weight from over his feet to over the seat by gently rocking the trunk

backward (Figure 1.9D). These movements are reversed when moving

from a sitting to a standing position.

Load, strain and stress

A load is any force or combination of forces applied to an object (Watkins

2007). There are three types of load: tension, compression and shear(Figure 1.10). Loads tend to deform the objects on which they act. Tension

is a pulling (stretching) load that tends to make an object longer and

A

B

C D

E F G

Figure 1.10 Types of load: (A) unloaded, (B) tension, (C) compression, (D) shear, (E) shearproducing friction, (F) bending, (G) torsion.

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thinner along the line of the force (Figure 1.10A and B). Compression is a

pushing or pressing load that tends to make an object shorter and thicker

along the line of the force (Figure 1.10A and C). A shear load is comprised of

two equal (in magnitude), opposite (in direction), parallel forces that tend

to displace one part of an object with respect to an adjacent part along

a plane parallel to and between the lines of force (Figure 1.10A and D). The

cutting load produced by scissors and garden shears is a shear load,

while the cutting load produced by a knife is a compression load. It is also

a shear load that forces one object to slide on another (Figure 1.10E). The

sliding or tendency to slide is resisted by a force called friction, which is

exerted between and parallel to the two contacting surfaces.

The three types of load frequently occur in combination, especially inbending and torsion (Figure 1.10A, F and G). An object subjected to bend-

ing experiences tension on one side and compression on the other. An

object subjected to torsion simultaneously experiences tension, com-

pression and shear.

In mechanics, the deformation of an object that occurs in response to

a load is referred to as strain. For example, when a muscle contracts it

exerts a tension load on the tendons at each end of the muscle and, con-

sequently, the tendons experience tension strain, i.e. they are very slightlystretched. Similarly, an object subjected to a compression load experiences

compression strain and an object subjected to a shear load experiences

shear strain. Strain denotes deformation of the intermolecular bonds that

comprise the structure of an object. When an object experiences strain, the

intermolecular bonds exert forces that tend to restore the original (unloaded)

size and shape of the object. The forces exerted by the intermolecular

bonds of an object under strain are referred to as stress. Stress is the resist-

ance of the intermolecular bonds to the strain caused by the load.The stress on an object resulting from a particular load is distributed

throughout the whole of the material sustaining the load. However, the

level of stress in different regions of the material varies depending upon

the amount of material sustaining the load in the different regions; the

more material sustaining the load, the lower the stress. Consequently,

stress is measured in terms of the average load on the plane of material

sustaining the load at the point of interest.

A load is any force or combination of forces applied to an object.

Strain is the deformation of an object that occurs in response to a

load. Stress is the resistance of the intermolecular bonds to the strain

caused by the load

KeyConcepts
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the tension stress on the Achilles tendon is equivalent to 1 944 000 Pa or

1.944 MPa (MPa megapascal 106Pa).

Compression stress

When standing barefoot, as in Figure 1.12A, the ground reaction force

exerts a compression load on the contact area of the feet. In an adult,

the contact area is approximately 260 cm2(both feet) (Hennig et al 1994).

For a person weighing 687 N (70 kgf ), the compression stress on the

contact area of the feet (on a level floor, contact area perpendicular to

the compression load) is 2.64 N/cm2, i.e.

compression stressN

cm

N/cm Pa

kPa

687

260

2 64 26 400

26 4

2

2.

. ((kPa kilopascal Pa) 103

By raising the heels off the ground the contact area is approximately

halved (Figure 1.12B). Since the compression load (body weight) is thesame as before, it follows that the compression stress on the reduced

contact area is approximately doubled. Compression stress is usually

referred to as pressure.

In some sports played on grass pitches, such as soccer and rugby,

the players wear studded boots to reduce the risk of slipping. Ideally,

the studs should sink fully into the playing surface when weight-bearing;

A B

Figure 1.12 Supporting area of the feet. (A) Normal upright standing posture, (B) standingupright with the heels off the floor.
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this would reduce the risk of slipping and ensure that the ground reac-

tion force is distributed evenly across the whole of the soles of the boots

(Figure 1.13A). However, when playing on a hard surface, the studs may

not sink fully into the playing surface such that the ground reaction force

will be transmitted directly by the studs and only indirectly by the soles

of the boots (Figure 1.13B). The combined area of the studs is very small

compared to the soles of the boots. Consequently, there will be anincrease in pressure on those parts of the feet directly above the studs.

The actual pressure on any part of each foot will depend upon the flex-

ibility of the soles of the boots; the more flexible the soles, the greater

the increase in pressure above the studs. Any kind of propulsive or brak-

ing movement (starting, stopping, turning) will increase the pressure even

more. As the pressure increases, so does the risk of injury to the feet.

There are 26 bones and about 40 joints in each foot. Consequently, most

movements of the foot involve a large number of joints. Boots with inflex-ible soles will seriously impair the natural movement of the feet and prob-

ably result in blisters, calluses and other disorders.

Shear stress

Many of the joints, especially those in the lower back and pelvis, are

subjected to shear load during normal everyday activities such as stand-

ing and walking. For example, in walking, there is a phase when one

leg supports the body while the other leg swings forward (Figure 1.14).

In this situation, the unsupported side of the body tends to move

downward relative to the supported side subjecting the pubic symphysis

joint to shear load. The area of the pubic symphysis in the plane of the

shear load is approximately 2 cm2. If the shear load at the instant shown

A B

Figure 1.13 Effect of hardness of playing surface on the distribution of the ground reactionforce on the sole of a studded boot. (A) Studs sink fully into the surface on a soft pitch,(B) studs do not sink fully into the surface on a hard pitch.

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Friction 23

in Figure 1.14 is, for example, 20 N, then the shear stress on the joint is

10 N/cm

2

, i.e.

shear stressN

cm

N/cm Pa kPa

20

2

10 100 000 100

2

2

Friction

When one object moves or tends to move across the surface of another,

there will be a force parallel to the surfaces in contact that will oppose the

movement or tendency to move. This force is called friction. Consider a

block of wood resting on a level table (Figure 1.15). The only forces acting

on the block are the weight of the block Wand the force Rexerted by

the table on the block. Since the block is at rest, Ris equal and opposite

A B

C

Figure 1.14 Shear load on the pubic symphysis resulting from single leg support whilewalking.

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to W (Figure 1.15A). If an attempt is made to push the block along the

surface of the table by applying a horizontal force P, the frictional force

Fbetween the contacting surfaces will begin to operate and oppose the

tendency of the block to move (Figure 1.15B). As P increases, so does F

until the block begins to move, i.e. Fhas a maximum value. This value is

directly proportional to the degree of roughness of the two surfaces in

contact and the force R. The three variables are related as follows:

F R . Eq. 1.1

where (Greek letter mu) is a measure of the roughness of the two sur-

faces in contact and is called the coefficient of friction between the twosurfaces. The force Ris the normal reaction force, i.e. the component of

the force exerted between the two surfaces that is perpendicular to the

plane of contact between the two surfaces.

The magnitude of depends upon the types of surface in contact

and whether the surfaces are sliding on each other. Surfaces are never

perfectly smooth and the minor irregularities of the contacting surfaces

W W

R R

P

F

A B

Figure 1.15 (A) The forces acting on a block of wood resting on a level table. (B) Theforces acting on a block of wood resting on a level table, but tending to slide horizontally.Wweight of the block, Rnormal reaction force, Phorizontal force applied to the sideof the block, Ffriction.

A B C

Figure 1.16 (A) Interdigitation of surface irregularities. (B) Slight separation of surfaces as aresult of sliding. (C) Complete separation of surfaces as a result of lubrication.

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Friction 25

interdigitate and resist sliding between the surfaces (Figure 1.16A).

To initiate sliding, the minor irregularities have to be dragged over each other.

In doing so, the surfaces tend to separate slightly, which reduces the

resistance to sliding, providing that the sliding is maintained (Figure

1.16B). Consequently, for any two surfaces in contact, (and therefore F)

will be slightly less when the surfaces are sliding on each other than

when the surfaces are not sliding on each other but tending to slide.

Therefore, for any two surfaces, there is a coefficient of limiting (static)

friction Land a coefficient of sliding (dynamic) friction S.

When no sliding occurs, the normal reaction force is distributed over

those parts of the adjacent surfaces that are in contact; this will include

the irregularities and some of the surfaces between the irregularities(Figure 1.16A). However, during sliding, the normal reaction force is exerted

almost entirely by the irregularities (Figure 1.16B). Consequently, during

sliding, the pressure exerted by the irregularities of one surface on the

other surface is likely to be considerably increased and result in wear of

the surface (similar to the effect of sandpaper on wood). The introduction

of a fluid between the surfaces tends to separate not only the surfaces,

but also the surface irregularities resulting in a considerable reduction in

friction and wear. This is the principle of lubrication (Figure 1.16C). In theabsence of lubrication, is about 0.250.50 for wood on wood, 0.15

0.60 for metal on metal, 0.200.60 for wood on metal and 0.40.9 for

wood on rubber (Serway & Jewett 2004).

Equation 1.1 shows that the amount of friction, limiting and sliding,

between two surfaces is independent of the area of contact when the

normal reaction force stays the same. The compression stress on the

surfaces will vary with the area of contact, but the amount of friction will

not change if the normal reaction force remains constant.The development of adequate friction between the human body and

the environment is essential for most actions of daily living, in particular,

body transport (friction between the feet and the floor) and manipulation of

objects (friction between the fingers and objects). The importance of the

need for adequate friction in these types of action is, perhaps, more obvi-

ous in sport where the quality of performance is likely to depend largely

upon the ability of the players to create adequate friction between feet

and playing surface and between hands and racket or other implement. In

such cases, adequate friction is maintained by using materials that have

appropriate coefficients of friction with the playing surface and with the

hands. For example, in volleyball, basketball, squash and badminton, the

soles of shoes are normally made of materials that will provide adequate

friction with the playing surface. It follows that for most indoor sports, the

playing surfaces should not be highly polished since this will reduce the

coefficient of friction and increase the possibility of slipping. However, too
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much friction is likely to impair performance and result in injury, especially

in sports that require rapid changes in speed and/or direction. Ideally, the

sole of the shoe should turn as the player turns, but excessive friction may

prevent the shoe turning and result in a twisting injury to the ankle or knee.

This is also a potential problem in sports played on grass pitches where

the players use studded boots. In these situations, the horizontal forces

produced between boots and playing surface are largely shear forces on

the studs rather than friction. However, if the studs are too long and sink

fully into the pitch, the sole of the boot may not turn as the player turns,

which will increase the risk of injury.

There are many non-sporting situations in which it is important to

ensure adequate friction in order to reduce the risk of injury. For example,an injured or aged person may rely heavily on walking sticks or crutches

for support. It is very important that the sticks or crutches do not slip

on the floor. Rubber has a high coefficient of friction with most materials

and, consequently, rubber tips are usually fitted to the ends of the walk-

ing sticks and crutches to reduce the risk of slipping.

Whereas the development of adequate friction between the human

body and the environment is essential for daily living, friction between

the different body tissues inside the body must be reduced as much aspossible in order to minimize the risk of injury or wear. The human body

is comprised of a number of different tissues that lie adjacent to each

other. Even the slightest movement involves a certain amount of sliding

of the various tissues on each other and, consequently, a certain amount

of friction between the tissues. Whenever friction develops, a certain

amount of heat is generated. Too much heat will injure or wear body

tissues. Minimizing friction is particularly important in the major weight-

bearing joints of the body, i.e. the hips, knees and ankles. The articularsurfaces of these joints are under considerable pressure even when the

person is just standing upright and any kind of propulsive movement of

the legs will increase the pressure even more. The greater the pressure,

the greater the friction between the articular surfaces.

Wearing of articular surfaces is similar to the wearing of brake pads

in the wheels of a motor vehicle. When braking occurs, an enormous

amount of friction and, therefore, heat is generated between brake pad

and wheel. Consequently, the brake pads eventually wear out and have

to be replaced. In a healthy joint, any wear is usually repaired by normal

metabolic processes. However, progressive joint degeneration will occur

when the rate of wear outpaces the rate of repair.

In machines, parts that slide on each other are usually highly polished

and friction is reduced even more by lubricating the sliding surfaces with

oil or grease. Similar mechanisms exist within the human body. All the

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Friction 27

freely moveable joints of the body are lined by synovial membrane that

produces synovial fluid (Figure 1.17). The latter is a transparent, viscous

fluid, resembling the white of an egg, that lubricates and nourishes the

articular surfaces (articular cartilage) of the joints. The articular surfaces

are normally extremely smooth so that in association with the synovial

fluid L0.01 and S0.003 (Serway & Jewett 2004). Consequently,

the amount of friction developed in healthy joints during normal move-

ments is usually extremely small.

The very low level of friction between the articular surfaces in a healthy

synovial joint is due to the viscosity (slipperiness) of the synovial fluid. The

viscosity of synovial fluid is largely due to its concentration of hyaluronic

acid. With age, the concentration of hyaluronic acid tends to decreasewhich, in turn, decreases the viscosity of the synovial fluid (Divine et al

2007). The decrease in viscosity increases L and S, which, in turn,

increases the friction between the articular surfaces. The increased friction

results in a progressive degeneration of the articular surfaces and, ultim-

ately, osteoarthritis. Osteoarthritic joints are characterized by synovial fluid

that contains 30%50% less hyaluronic acid than healthy joints (eOrthopod

2008). One form of treatment for osteoarthritis, referred to as viscosup-

plementation, involves artificially increasing the concentration of hyaluronicacid in synovial fluid by injecting it into the cavity of the affected joints.

Humerus

Joint capsule

Synovial membrane

Radius

UlnaArticular

cartilage

Synovial fluid

occupying

the joint cavity

Figure 1.17 Vertical section through the elbow joint.
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response to a prolonged increase in friction. For example, a bursa may

form between the Achilles tendon and the skin; this is referred to as the

posterior Achilles tendon bursa (Figure 1.18).

Whereas the development of adequate friction between the human

body and the environment is essential for daily living, friction between

the different body tissues inside the body must be reduced as much

as possible in order to minimize the risk of injury or wear

KeyConcepts

Musculoskeletal system function

Posture refers to the orientation of body segments to each other and

is usually applied to static or quasi-static positions such as sitting and

standing. When standing upright there are two forces acting on the

body, body weight and the ground reaction force (Figure 1.19A). The

ground reaction force is the force exerted by the ground on the body.When standing upright the ground reaction force is equal in magnitude

but opposite in direction to body weight. The combined effect of body

weight and the ground reaction force is a compression load that tends

to collapse the body in a heap on the ground. This compression load

increases with any additional weight carried by the body (Figure 1.19B).

To prevent the body from collapsing while simultaneously bringing about

desired movements, the movements of the various joints need to be

carefully controlled by coordinated activity between the various muscle

groups. For example, when standing upright the joints of the neck, trunk

and legs must be stabilized by the muscles that control them, other-

wise the body would collapse (Figure 1.20). Consequently, the weight of

the whole body is transmitted to the floor by the feet, but the weights of

the individual body segments above the feet (head, arms, trunk and legs)

are transmitted indirectly to the floor by the skeletal chain formed by the

bones and joints of the neck, trunk and legs.

Transmitting body weight to the ground while maintaining an upright

body posture illustrates the essential feature of musculoskeletal func-tion, i.e. the generation (by the muscles) and transmission (by the bones

and joints) of forces. In biomechanical analysis of human movement,

the forces generated and transmitted by the musculoskeletal system

are referred to as internal forces, and forces that act on the body from

external sources, such as body weight, ground reaction force, water
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Musculoskeletal system function 31

resistance and air resistance, are referred to as external forces. The mus-

culoskeletal system generates and transmits internal forces to counteract

the effects of gravity and create the ground reaction forces (and propul-

sion forces in water) necessary to maintain upright posture, transport the

body and manipulate objects, often simultaneously (Watkins 2007).

A B

W

F1

W

B

F2

Figure 1.19 Compression load on the body in upright postures. Wbody weight;Bweight of object; F1, F2ground reaction forces.

The function of the musculoskeletal system is to generate and transmit

forces to enable us to maintain an upright or partially upright posture,

move from one place to another and manipulate objects

KeyConcepts
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1

Neck flexorsTrunk extensors

Hip extensors and

knee flexors

Knee flexors and

ankle plantar flexors

Trunk flexors

Hip flexors and

knee extensors

Ankle dorsi-flexors

Figure 1.20 Location of the main muscle groups responsible for maintaining standingposture.

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volume, area, time, temperature, mass, distance and speed. Quantities

that require specification in both magnitude and direction are called vec-

tor quantities. These include displacement (distance in a given direction),

velocity (speed in a given direction), acceleration and force. In a vector

diagram, each vector is represented by an arrow; the length of the arrow,

with respect to an appropriate scale, corresponds to the magnitude of

the vector and the orientation of the arrow, with respect to an appropri-

ate reference axis (usually horizontal or vertical) indicates the direction.

All quantities in the physical and life sciences can be categorized

as either scalar or vector quantities. Quantities that can be com-

pletely specified by their magnitude (size) are called scalar quantities.

Quantities that require specification in both magnitude and direction

are called vector quantities

KeyConcepts

Force vectors and resultant forceWhen standing upright, there are three forces acting on the human body,

body weight W acting at the centre of gravity of the body, the ground

reaction force FLon the left foot and the ground reaction force FRon the

right foot (Figure 1.22A). Figure 1.22Bshows the corresponding vector dia-

gram; the resultant ground reaction force (resultant of FLand FR) is equal

in magnitude but opposite in direction to W, i.e. the resultant force acting

on the body is zero. InFigure 1.22C

the force F1 is the resultant groundreaction force (resultant of FL and FR) and Figure 1.22D shows the cor-

responding vector diagram. To start walking or running (or move hori-

zontally by any other type of movement such as jumping or hopping)

the body must push or pull against something to provide the necessary

resultant force to move it in the required direction. In walking and run-

ning, forward movement is achieved by pushing obliquely downward and

backward against the ground. Provided that the foot does not slip, the

leg thrust results in a ground reaction force directed obliquely upward and

forward; this is F2in Figure 1.22E. The resultant force Rof Wand F2moves

the body forward while maintaining an upright posture, i.e. the centre of

gravity of the body is accelerated in the direction of R. The correspond-

ing vector diagram is shown in Figure 1.22F. The vector diagram in Figure

1.22Fillustrates the vector chain method of determining the resultant of a

number of vectors; the component vectors (Wand F2) are linked together
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referred to as the opposite side, sidebis referred to as the adjacent side

and side c is the hypotenuse, the side of the triangle opposite the right

angle.

The sine of qis defined as the ratio of the opposite side to the hypot-

enuse, i.e.

sine

opposite side

hypotenuse

a

c

The cosine of qis defined as the ratio of the adjacent side to the hypot-

enuse, i.e.

cosineadjacent side

hypotenuse

b

c

The tangent of qis defined as the ratio of the opposite side to the adja-

cent side, i.e.

tangentopposite side

adjacent side

a

b

a

b

c

Figure 1.23 Definition of sine, cosine and tangent in a right-angled triangle:

sine sine

cosine cosine

tangent

a

c

b

cb

c

a

ca

b

tanggent b

a

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Vector and scalar quantities 37

Most electronic calculators provide a range of trigonometric ratios including

sine (sin), cosine (cos) and tangent (tan). Alternatively, tables of sine, cosine

and tangent (for angles between 0 and 90) can be obtained in publications

such as Castle (1969). The lengths of sides and sizes of angles in right-

angled triangles can be calculated using sine, cosine and tangent functions

provided that two sides or one side and one other angle are known. With

reference to Figure 1.23, for example, if c10 cm and q30, the lengths

of sidesaandband the size of angle can be determined as follows.

1. Calculation of the length of sidea

ac

a c

a c

sin

sin (i.e. c multiplied by sin )sin

.. 30

From sine tables, sin 30 0.5 (i.e., the ratio of the length of side a

to the length of side c is 0.5). Since c10 cm and sin 30 0.5, it

follows that

a

a

10 0 55

cmcm

.

2. Calculation of the length of sideb

b

c

b c

b c

cos

cos (i.e. c multiplied by cos )cos

.. 30

From cosine tables, cos 30 0.866 (i.e., the ratio of the length

of side b to the length of side c is 0.866). Since c10 cm and

cos 30 0.866, it follows that

b

b

10 0 8668 66

cmcm

..

3. Calculation of angle

Angle can be determined a number of ways:

i. The sum of the three angles in any triangle (with or without a right

angle) is 180. Since the sum of qand the right angle is 120, it

follows that 180120 60

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Vector and scalar quantities 39

horizontal. In Figure 1.24B, Fhas been replaced by its vertical FVandhorizontal FHcomponents. From Figure 1.24B

F F

F F

F F

V

V

H

sin

sin kgf kgf

cos

/

. . .

/

70

70 80 0 9397 75 17

7

00

70 80 0 3420 27 36

F FH cos kgf kgf . . .

2. Calculate the vertical component RVand horizontal component RHof

the resultant force Racting on the man

W

70

F FV

FH

W

RV RH

R

A CB

Figure 1.24 The forces acting on a man just after starting to walk. Wbodyweight 70 kgf. F80 kgf at 70 to the horizontal. Rresultant force 27.87 kgf at10.7 to the horizontal.

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Moment of a force 41

the block Wwill tend to rotate the block about the supporting edge back

to its original resting position in Figure 1.25A. The tendency to restore

the block to its original position is the result of the moment (or turn-

ing moment) of Wabout the axis of rotation BC. The magnitude of the

moment of Wabout the axis BC is equal to the product of Wand the

perpendicular distance dbetween the axis BC and the line of action of W(Figure 1.25B), i.e.

moment of about axis AB multiplied by )W W d W d . (

If W2 kgf and d0.1 m, then

moment of about axis AB kgf m kgf.mW 2 0 1 0 2. .

As 2 kgf 19.62 N, then

moment of about axis AB N m N.mW 19 62 0 1 1 962. . .

The N.m (newton metre) is the unit of moment of force in the SI system

(see Table 1.1).

In general, when a force F acting on an object rotates or tends to

rotate the object about some specified axis, the moment of Fis defined

as the product of Fand the perpendicular distance dbetween the axis

of rotation and the line of action of F, i.e. moment of F F.d.The axis

of rotation is often referred to as the fulcrum and the perpendicular dis-

tance between the line of action of the force and the axis of rotation is

A

A

B

B

d

D C

W

W

A B

Figure 1.25 The turning moment of a force. (A) Block of wood at rest on base of support

ABCD. (B) Turning moment W.dof the weight of the block Wtending to restore the block toits original resting position after being tilted over on edge BC. dmoment arm of Waboutedge BC.

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usually referred to as the moment arm of the force. The moment of a

force is sometimes referred to as torque. For a given moment of force,

the greater the force, the smaller the moment arm of the force and vice

versa. For example, in trying to push open a heavy door, much less force

will be required if the force is applied to the side of the door furthest away

from the hinges, i.e. a large moment arm, than if the force is applied tothe door close to the hinges, i.e. a small moment arm (Figure 1.26).

d2

d1

F1

F2

Figure 1.26 Effect of length of moment arm on magnitude of force needed to produce aparticular moment of force to open a door. F1.d1F2.d2. If d23d1, then F13F2.

The moment of a force is the product of the magnitude of the force

and the perpendicular distance between the line of action of the force

and the axis of rotation

KeyConcepts

Clockwise and anticlockwise moments

When an object is acted upon by two or more forces which tend to

rotate the object, the actual amount and speed of rotation that occurs

will depend upon the resultant moment acting on the object, i.e. the

resultant of all the individual moments.

Figure 1.27shows the posterior and lateral aspects of the right foot of

a runner at foot-strike. In this example, the runner is a rear foot striker

and contact with the ground is made with the outside of the heel. In this

situation the ground reaction force will tend to be directed upward, later-

ally and posteriorly. Consequently, when viewed from the rear, the ground

reaction force will exert an anticlockwise moment on the heel about

an anteroposterior axis through the ankle that tends to evert the heel,

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146

Equilibrium

In the situation illustrated in Figure 1.28A, the moments of the weights

of the two boys acting about the fulcrum of the seesaw are equal and

opposite such that the resultant moment acting on the seesaw is zero

and the seesaw is at rest. As the seesaw is at rest, the resultant force

on the seesaw is also zero. Consequently, the resultant downward force

on the seesaw, i.e. the weights of the seesaw and the two boys, must

be counteracted by one or more forces whose resultant is equal and

opposite to the weights of the seesaw and the two boys. In this case,

the counteracting force is a single force Rexerted by the seesaw support

through the fulcrum. Figure 1.28Bshows a free body diagram of the see-saw (a diagram showing all of the external forces acting on the seesaw)

in the situation illustrated in Figure 1.28A. As WA40 kgf, WB30 kgf

and WS20 kgf, then R WAWBWS90 kgf.

With regard to linear motion, an object is in equilibrium when the result-

ant force acting on the object is zero. With regard to angular motion, an

object is in equilibrium when the resultant moment acting on the object is

zero. These two equilibrium conditions are the basis for calculating forces

acting on different parts of a multi-segment system, such as muscleforces and joint reaction forces in the human body.

Achilles tendon force and ankle joint reactionforce in upright standing

Figure 1.29Ashows a man standing upright with the line of action of his

weight slightly in front of his ankle joints. Consequently, body weight

will exert an anticlockwise moment about the axis of plantar flexion-

dorsiflexion (A) tending to rotate his body forward. In this posture, stabil-

ity is maintained largely by isometric contraction of the ankle joint plantar

flexors, as shown in the simple two-segment model in Figure 1.29Bwhere

Wbody weight, R the ground reaction force and F the force in

the Achilles tendons (both legs). If it is assumed that each leg supports

half of body weight, Figure 1.29Cshows a free body diagram of one foot

where R1ground reaction force, Tforce in the Achilles tendon act-

ing an angle of 85 to the horizontal and Jankle joint reaction force.As the weight of the foot (

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Achilles tendon force and ankle joint reaction force in upright standing 47

resultant moment on the foot is zero. Consequently, taking moments

aboutA, it follows that

R d T d 1 1 2. . Eq. 1.2

where d1 moment arm of R1 about A and d2 moment arm of T

aboutA.

If W70 kgf, then R135 kgf. When d15 cm, d2 will also be

about 5 cm. Consequently, from equation 1.2

T R d

d

1 1

2

35 5

535

. kgf cm

cmkgf

Figure 1.29Dshows a free body diagram of the foot in which Jand Thave

been replaced by their horizontal (JH, TH) and vertical (JV, TV) compo-

nents. As Tacts at 85 to the horizontal then

T T

T T

T T

H

H

V

coscos kgf kgf

sin

/. . .

/

8585 35 0 0871 3 05

85

T TV sin kgf kgf. . .85 35 0 9962 34 87

A B C

D

E

W

W

F

R

A

R

R1T

J 85

d1

JV

JV

TV

TH

JH

JH

R1

d2

Figure 1.29 Achilles tendon force and ankle joint reaction force when standing upright.
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1 ELEMENTARY BIOMECHANICS

A

B

E

R

R

E

dE

dR

Crowbar

Figure 1.31 (A) Use of a crowbar to open a box. (B) The corresponding force-moment armdiagram. Eforce exerted on the crowbar by the person using it; dEmoment arm of E;

Rresistance force exerted on the crowbar by the lid of the box; dRmoment arm of R.

A lever is an object that can be made to rotate about a fulcrum in

order to exert a force on another object

KeyConcepts

Mechanical advantage

The mechanical advantage (MA) of a lever is a measure of its efficiency

in terms of the amount of effort needed to overcome a particular resist-

ance, i.e.

MA magnitude of resistancemagnitude of effort

length

R

E

oof moment arm of

length of moment arm ofE

R

E

R

d

d

50

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Load on the musculoskeletal system 51

The greater the mechanical advantage of a lever, the smaller the effort

needed to overcome a particular resistance.

Load on the musculoskeletal system

The open-chain arrangement of the bones (four peripheral chains the

arms and legs attached onto a central chain the vertebral column)

and skeletal muscles (closely aligned to the bones) maximizes the range

of possible body postures. However, the price that the body pays for this

movement capability is low mechanical advantage. Most of the skeletal

muscles are inserted close to the joints that they control and, as such,

have shorter moment arms than the resistance forces they counteract,i.e. the skeletal muscles usually have to exert much larger forces than the

weights of the body segments they control. Furthermore, as illustrated

in Figure 1.29, joint reaction forces are determined by muscle forces; the

larger the muscle forces, the larger the joint reaction forces. For example,

in walking, the peak hip, knee and ankle joint reaction forces in adults

are normally in the range of 5 to 6, 3 to 8, and 3 to 5 times body weight,

respectively (Nigg 1985). The more dynamic the activity, the greater the

muscle forces and, therefore, the greater the joint reaction forces. Forexample, in fast running (800 m pace), the peak knee and ankle joint

reaction forces in an adult are likely to be in the region of 20 and 8 times

body weight, respectively (Nigg 1985).

In any body position other than the relaxed recumbent position, the

components of the musculoskeletal system (muscles, bones, joints) are

likely to be subjected to considerable load. In response to the load the

musculoskeletal components experience strain; the greater the force,

the greater the strain. Under normal circumstances the musculoskeletal

components adapt their size, shape and structure to the time-averaged

forces exerted on them in order to more readily withstand the strain.

However, excessive strain will result in injury and/or degeneration.

Consequently, there is an intimate relationship between the structure and

function of the musculoskeletal system (Watkins 1999).

The open-chain arrangement of the skeleton maximizes the range of

possible body postures, but only at the expense of low mechanical

advantage; the muscles, bones and joints are subjected to very high

forces in virtually all postures other than lying down

KeyConcepts
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ELEMENTARY BIOMECHANICS1

Review questions

1. Define the following terms: force, contact force, attraction force,resultant force, mechanics, biomechanics, mass, inertia, volume,

density, stiffness, strength, kinematics, kinetics.

2. Describe the two ways in which forces tend to affect bodies.

3. Describe the four main sub-disciplines of mechanics.

4. Describe the two fundamental forms of motion.

5. List the base units for length, mass and time in the International

System of Units.

6. With regard to musculoskeletal system function, describe the rela-tionship between external and internal forces.

7. Briefly describe the three broad categories of movement brought

about by the musculoskeletal system.

8. With reference to recumbent posture and standing posture, explain

the difference between direct and indirect transmission of the weight

of body segments to the support surface.

9. Describe how direct and indirect transmission of the weight of body

segments to the support surface likely affects the degree of activity

in the muscles.

10. Describe the main advantage and disadvantage of the open-chain

arrangement of the skeleton.

References

Bagga H, Burkhardt D, Sambrook P, March L (2006) Longterm effects of

intraarticular hyaluronan on synovial fluid in osteoarthritis of the knee.Journal of Rheumatology 33:94650.

Castle F (1969) Five-figure logarithmic and other tables. Macmillan, London.

Divine PG, Zazulak BT, Hewett TE (2007) Viscosupplementation for kneeosteoarthritis: a systematic review. Clinical Orthopaedics and RelatedResearch 455:11322.

Dempster WT (1965) Mechanisms of shoulder movement. Archives ofPhysical Medicine and Rehabilitation 46:4970.

eOrthopod (2008) Viscosupplementation for osteoarthritis of the knee.Available online at: http://eorthopod.com/public/patient_education/6515/viscosupplementation for the knee.html

Elert G, ed (2000) The physics fac

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